Math. Models Methods Appl. Sci. 3 (1993), 711-723.
Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA
Maurizio Paolini
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy
Claudio Verdi
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy
The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter $\eps>0$. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order $\O(\epsq)$ are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.